_______________________________________________ LECTURE 9 Hydraulic machines III and EM machines ________________________________________ © 2002 MIT PSDAM LAB

2.000 DC Permanent magnet electric motors _______________________________________________ Topics of todays lecture: Project I schedule revisions Test Bernoullis equation Electric motors Review I x B Electric motor contest rules (optional contest) Class evaluations ________________________________________ © 2002 MIT PSDAM LAB

Project schedule updates _______________________________________________ Approx START WHAT DUE PTS 07 March Project mgmt spread sheet 14 March [ 20 ] 12 March HMK 6: 1 page concept & equations 02 April [ 80 ] + SIMPLE 1 page explanation 19 March Gear characteristics 02 April [ 10 ] 1 page explanation 19 March CAD files & DXF files 09 April (via zip disk) [ 90 ] Σ: 200 ________________________________________ © 2002 MIT PSDAM LAB

_______________________________________________ BERNOULLIS EQUATION ________________________________________ © 2002 MIT PSDAM LAB

Streamlines _______________________________________________ Streamline: Line which is everywhere tangent to a fluid particles velocity. For a steady flow, stream lines do not move/change A stream line is the path along which a fluid particle travels during steady flow. For one dimensional flow, we can assume that pressure (p) and velocity (v) have the same value for all stream lines passing through a given cross section Bernoullis equation for steady flow, constant density: ________________________________________ © 2002 MIT PSDAM LAB

Bernoulli derivation _______________________________________________ For two cross section (ends of control volume) located dx apart: ______________________________________ ________________________________________ © 2002 MIT PSDAM LAB

Bernoulli derivation _______________________________________________ Stead flow momentum equation for Control Volume From F = m a following a fluid mass For a stead, there is no stored mass ________________________________________ © 2002 MIT PSDAM LAB

Bernoulli derivation _______________________________________________ Pressure force: ________________________________________ © 2002 MIT PSDAM LAB

Bernoulli derivation _______________________________________________ Gravity: ________________________________________ © 2002 MIT PSDAM LAB

Bernoulli derivation _______________________________________________ Summation of pressure and gravity forces: ________________________________________ © 2002 MIT PSDAM LAB

Bernoulli derivation _______________________________________________ Equating momentum flow and applied forces: ________________________________________ © 2002 MIT PSDAM LAB

Bernoullis Equation: Assumptions _______________________________________________ Flow along streamline B.E. can only be used between points on the SAME streamline. Inviscid flow: Loss due to viscous effects is negligible compared to the magnitudes of the other terms in Bernoullis equation. Bernoullis equation cant be used through regions where fluids mix: Mixed jets & wakes (flow want to break up, swirl… resulting shear dissipates energy) Pumps & motors Other areas where the fluid is turbulent or mixing. Mixing = Cant Use Bernoullis Equation You can not use Bernoullis Equation through jets or turbulent areas Stead state Velocity of the flow is not a function of time, BUT!!! it can be a function of position. Incompressible ________________________________________ © 2002 MIT PSDAM LAB

Bernoullis Example – Pipe of variable diameter _______________________________________________ Given, find the pressure difference between A & B as a function of, and Is this a rise or drop in pressure? Assumptions (along streamline, inviscid, stead state, incompressible) Bernoullis equation between points A and B: ________________________________________ © 2002 MIT PSDAM LAB

Bernoullis Example – Pipe of variable diameter _______________________________________________ Volume flow rate equality: ________________________________________ © 2002 MIT PSDAM LAB

_______________________________________________ DC PERMANENT MAGNET MOTOR ________________________________________ © 2002 MIT PSDAM LAB

Vector cross product review _______________________________________________ Vector cross products: Mutual perpendicularity: Magnitude: When: A & B are PARALLEL, the magnitude of (A X B) is 0 A & B are PERPENDICULAR, the magnitude (A X B) is maximized ________________________________________ © 2002 MIT PSDAM LAB

Magnetic force on a conductor (wire) _______________________________________________ Force on a conductor carrying a current through a magnetic field: Where: _______________________________________________________________ ________________________________________ © 2002 MIT PSDAM LAB

Magnetic torque on a simple electric machine _______________________________________________ Force on a conductor carrying a current through a magnetic field: For wire 3, always = so always = 1 Force on wires 1 (to left) and 2 (to right) do not act to make wire rotate ________________________________________ © 2002 MIT PSDAM LAB

Magnetic torque as a function of position _______________________________________________ ________________________________________ © 2002 MIT PSDAM LAB

What does the torque vs θ curve look like? [2 mins] _______________________________________________ ________________________________________ © 2002 MIT PSDAM LAB

Torque on simple wire loop carrying current _______________________________________________ Torque curve of simple loop Side view of simple loop ________________________________________ © 2002 MIT PSDAM LAB

Keeping the machine in motion _______________________________________________ How to keep the machine moving Once the wire passes horizontal, Tm tries to stop the wire from rotating. To keep the wire rotating, we must either shut off the current or reverse the current. If we turn off the current, the wire will continue to rotate due to its inertia. If we reverse the current direction when the wire reaches horizontal, Tm will act to keep the wire spinning If current continues in the same direction, Changing current direction will change the direction of Fm Tm tries to stop wire from spinning.. This in turn switches the direction of Tm. Tm will now act to keep the wire spinning. ________________________________________ © 2002 MIT PSDAM LAB

Torque on switched wire loop carrying current _______________________________________________ Torque curve of switched loop Side view of switched loop ________________________________________ © 2002 MIT PSDAM LAB

DC Permanent magnet electric motor build & contest _______________________________________________ In your kit you will find materials to build a simple electric motor How it works: Motor current shuts off when torque becomes negative Rotor inertia carries rotor until current turn on Repeated cycle keeps the motor spinning. We will have a contest (in your lab sessions) to determine winner How do you maximize energy input? How do you minimize losses? Friction You may need to try various things Class record = 1800 RPM! Prizes Fastest motor = $20 Cheesecake Factory gift certificate Record breaker = Keep Lego kit at end of class ________________________________________ © 2002 MIT PSDAM LAB

Torque on switched wire loop carrying current _______________________________________________ Torque curve of switched loop Side view of switched loop ________________________________________ © 2002 MIT PSDAM LAB

DC Permanent magnet electric motor build & contest _______________________________________________ Contest rules: The contest is OPTIONAL Motor may only contain the materials in your kit and a roll of life savers You may use the contents of your tool kits to help shape/make the motor You may not use any other tools/machines to make the motor Any wire coil must be wound around the battery or the roll of life savers You may obtain up to 3 ft of additional wire from a TA if you need it Your motor may only be powered by our power source (fresh D battery) We will test them in lab next week ________________________________________ © 2002 MIT PSDAM LAB